Table of Contents
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 417623, 10 pages
http://dx.doi.org/10.1155/2014/417623
Research Article

Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

1Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece
2Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou Street, 35100 Lamia, Greece

Received 24 February 2014; Accepted 31 March 2014; Published 4 May 2014

Academic Editors: F. Ding, L. Guo, and H. C. So

Copyright © 2014 Nicholas Assimakis and Maria Adam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. D. O. Anderson and J. B. Moore, Optimal Filtering, Dover Publications, New York, NY, USA, 2005.
  2. N. Assimakis and M. Adam, “Global systems for mobile position tracking using Kalman and Lainiotis filters,” The Scientific World Journal, vol. 2014, Article ID 130512, 8 pages, 2014. View at Publisher · View at Google Scholar
  3. F. Ding, “Combined state and least squares parameter estimation algorithms for dynamic systems,” Applied Mathematical Modelling, vol. 38, no. 1, pp. 403–412, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  4. F. Ding and T. Chen, “Hierarchical identification of lifted state-space models for general dual-rate systems,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 6, pp. 1179–1187, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  5. B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter, Artech House, Boston, Mass, USA, 2004.
  6. M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice Using MATLAB, John Wiley & Sons, Hoboken, NJ, USA, 3rd edition, 2008.
  7. N. Assimakis and M. Adam, “Kalman filter Riccati equation for the prediction, estimation and smoothing error covariance matrices,” ISRN Computational Mathematics, vol. 2013, Article ID 249594, 7 pages, 2013. View at Publisher · View at Google Scholar
  8. J. R. P. de Carvalho, E. D. Assad, and H. S. Pinto, “Kalman filter and correction of the temperatures estimated by PRECIS model,” Atmospheric Research, vol. 102, no. 1-2, pp. 218–226, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Furrer and T. Bengtsson, “Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants,” Journal of Multivariate Analysis, vol. 98, no. 2, pp. 227–255, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Y. Teruyama and T. Watanabe, “Effectiveness of variable-gain Kalman filter based on angle error calculated from acceleration signals in lower limb angle measurement with inertial sensors,” Computational and Mathematical Methods in Medicine, vol. 2013, Article ID 398042, 12 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. Han, “A closed-form solution to the discrete-time Kalman filter and its applications,” Systems & Control Letters, vol. 59, no. 12, pp. 799–805, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. D. R. Vaughan, “A nonrecursive algebraic solution for the disczte Riccati equation,” IEEE Transactions on Automatic Control, vol. 15, no. 5, pp. 597–599, 1970. View at Google Scholar · View at Scopus
  13. R. Leland, “An alternate calculation of the discrete-time Kalman filter gain and Riccati equation solution,” Transactions on Automatic Control, vol. 41, no. 12, pp. 1817–1819, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. N. Assimakis, “Discrete time Riccati equation recursive multiple steps solutions,” Contemporary Engineering Sciences, vol. 2, no. 7, pp. 333–354, 2009. View at Google Scholar
  15. N. D. Assimakis, D. G. Lainiotis, S. K. Katsikas, and F. L. Sanida, “A survey of recursive algorithms for the solution of the discrete time riccati equation,” Nonlinear Analysis: Theory, Methods and Applications, vol. 30, no. 4, pp. 2409–2420, 1997. View at Google Scholar · View at Scopus
  16. N. Assimakis, S. Roulis, and D. Lainiotis, “Recursive solutions of the discrete time Riccati equation,” Neural, Parallel and Scientific Computations, vol. 11, no. 3, pp. 343–350, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. G. Lainiotis, N. D. Assimakis, and S. K. Katsikas, “A new computationally effective algorithm for solving the discrete Riccati equation,” Journal of Mathematical Analysis and Applications, vol. 186, no. 3, pp. 868–895, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. D. G. Lainiotis, N. D. Assimakis, and S. K. Katsikas, “Fast and numerically robust recursive algorithms for solving the discrete time Riccati equation: the case of nonsingular plant noise covariance matrix,” Neural, Parallel and Scientific Computations, vol. 3, no. 4, pp. 565–583, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. M. Liyanage and I. Sasase, “Steady-state Kalman filtering for channel estimation in OFDM systems utilizing SNR,” in Proceedings of the IEEE International Conference on Communications (ICC '09), pp. 1–6, Dresden, Germany, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. T. R. Kronhamn, “Geometric illustration of the Kalman filter gain and covariance update algorithms,” IEEE Control Systems Magazine, vol. 5, no. 2, pp. 41–43, 1985. View at Google Scholar · View at Scopus
  21. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 2005.